Michelle L. Coote et al., Polymer, 44, (2003), 7689 - 7700.

Neutron reflectometry investigation of polymer–polymer reactions at the

interface between immiscible polymers

Michelle L. Cootea,1, Duncan H. Gordona,2, Lian R. Hutchingsa, Randal W. Richardsa,*,3,Robert M. Dalglieshb

aInterdisciplinary Research Centre in Polymer Science and Technology, University of Durham, Durham DH1 3LE, UKbISIS Science Division, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QZ, UK

Received 15 May 2003; received in revised form 18 August 2003; accepted 10 September 2003

Abstract

Primary amine end functionalised deuteropolystyrene has been mixed with unmodified hydrogenous polystyrene and a thin film placed on

top of a film of an acrylic polymer that either has carboxylic acid groups located at one end of each molecule or as substituents on each repeat

unit. After holding at 453 K for defined times, the interfacial excess layer at the interface between the two polymers has been quantitatively

analysed using neutron reflectometry and the extent of grafting of the deuteropolymer at the interface determined. Whilst maintaining the

concentration of carboxylic acid units constant (fixed reacting groups) the extent of grafting increases with concentration of the

functionalised deuteropolystyrene in the polystyrene layer. On changing the molecular weight of the functionalised deuteropolystyrene but

maintaining the molar concentration of reactive end groups constant, the extent of grafting is larger for the lower molecular weight polymer.

Although, the qualitative variation of the extent of grafting with time is in agreement with theories for interfacial grafting, exact

correspondence cannot be obtained. The initial rate of grafting corresponds to second order rate constants of ,0.1–0.2 l mol21 s21 but

saturation of grafting is evident at far lower values (and hence earlier in the reaction process) than predicted by theory. Moreover, this

saturation extent of grafting is at a level much lower than anticipated if brush-like layer formation is encouraged by interfacial grafting.

q 2003 Elsevier Ltd. All rights reserved.

Keywords: Interfacial reactions; Immiscible polymers; Kinetics; Neutron reflectometry

1. Introduction

Interfaces in immiscible polymer blends are the locus of

mechanical failure and the improvement in properties

anticipated on dispersing one polymer in another often

may not result in the dispersion. Improving the mechanical

properties by adding a block copolymer of the two polymers

has long been known and the increase in mechanical

strength at such interfaces has been experimentally demon-

strated [1]. However, the block copolymer is another

component that needs to be dispersed in the mixture and

may itself form micelles [2,3] and thus become effectively

inactive with regards to the primary reason for their

addition. Although the use of random copolymers [4–9]

may overcome this micellisation problem and strengthen the

interface such copolymers may not locate at the interface in

sufficient quantity due to thermodynamic influences on the

diffusion coefficient.

A more attractive method of strengthening the interface

between immiscible polymers is by reactive processing

[10–12] where each phase contains a percentage of polymer

molecules with reactive functionalities that will combine

with each other. Consequently, due to the intrinsic

immiscibility of the two polymers reaction can only take

place at the interface leading to copolymer formation and

subsequent strengthening of the interface. Ultimately, if this

grafting reaction at the interface goes to a sufficiently high

extent, the interfacial tension may be reduced to such a

degree that the interface becomes unstable, roughens and

‘droplets’ escape into the surrounding phase [13]. This latter

effect may be desirable, a dispersion of small particles

0032-3861/$ - see front matter q 2003 Elsevier Ltd. All rights reserved.

doi:10.1016/j.polymer.2003.09.023

Polymer 44 (2003) 7689–7700

www.elsevier.com/locate/polymer

1 Present address: Research School of Chemistry, Science Road,

Australian National University, Canberra, A.C.T. 0200, Australia.2 Present address: School of Engineering (Metallurgy and Materials), The

University of Birmingham, Edgbaston, Birmingham, B15 2TT.3 Present address: EPSRC, Polaris House, Northstar Avenue, Swindon

SN2 1EJ.

* Corresponding author.

http://www.elsevier.com/locate/polymer

leading to improved mechanical properties. An assessment

of the probability for the success of this approach requires

an understanding of the intrinsic kinetics of the grafting

reaction. Some questions that arise include; to what extent

may the rate of grafting be diffusion controlled and at what

stage does diffusion control become evident; what role does

the concentration and molecular weight of reactive polymer

play in defining the grafting kinetics? Does saturation (i.e.

prevention of further interfacial reaction) intervene to

control the kinetics at some point? There have been a

number of theoretical studies of interfacial grafting of

varying degrees of complexity [14–20] and we provide a

precis of those that are relevant in the succeeding section.

Experimental investigations that conform to a greater or

lesser extent to the conditions used by theoretical

approaches are rare. Although, conforming closely to actual

conditions used in reactive processing, those experimental

investigations [10] where mixing was used are not suitable

to observe the fundamental kinetics because the interface is

continually renewed. Comparison of the extent or degree of

grafting, S (chains per unit area), with the predictions of

theory requires that the interfacial region be well defined

and of unchanging area. A priori we anticipate the grafted

layer thickness in either polymer phase to have dimensions

of circa the radius of gyration of the block early in the

reaction but as saturation is approached this layer thickness

may increase markedly approximating to a polymer brush

layer. Consequently, the experimental techniques employed

need to be able to distinguish an excess polymer layer at the

interface over length scales of ,50–500 A depending on

molecular weight and extent of grafting. One technique that

covers this range admirably and with a resolution of circa

20 A is neutron reflectometry [21,22], a disadvantage is that

deuterated polymers are required. We report here the

application of neutron reflectometry to investigate the

reaction between end functionalised polystyrene and

polymethyl methacrylate at the interface between thin

films of the two polymers. Aspects investigated include

concentration of reactive ends and molecular weight of

polymer.

2. Theory

Tethering of polymer chains by the reaction of a

functional end with a fixed reactive site constitutes a

grafting of the functional ended polymer to the surface

bearing the reactive site [23–28]. The progress of the

reaction can be followed by the increase in grafting density

(number of molecules per unit area), S; with time and as S

increases an interfacial excess of the reacting polymer is

formed, the relation between interfacial excess, zp; and

grafting density being given by

zp ¼ NS=r0 ð1Þ

where N is the degree of polymerisation of the reacting

polymer that has a segment number density of r0: There are

currently three major theoretical descriptions of the kinetics

of reactions at the interface between immiscible end

functionalised polymers leading to grafting of the interface

and formation of a block copolymer [15,29,30]. The

situation is shown schematically in Fig. 1, with interfacial

grafting leading to the formation of a brush-like polymer

layer when S exceeds a critical value.

Kramer [16] presents a model for the case where there

are an infinite number of reactive sites fixed at the interface

with a second polymer that has a finite concentration of end-

functionalised polymer. Some of this polymer is presumed

Fig. 1. Schematic illustration of the formation of excess layer due to

interfacial reaction between immiscible polymers containing a low

concentration of end functionalised molecules at an interface with fixed

reactive groups. (A) As formed bilayer, (B) early stages of reaction with

isolated grafted chains in mushroom conformation, (C) later stages where

grafting density has increased to the extent that a brush like layer is formed.

M.L. Coote et al. / Polymer 44 (2003) 7689–77007690

to have reacted and a brush like layer is already in existence.

Unreacted chains have to penetrate this brush-like layer to

allow the functional end to approach within a critical

distance of the interface (,statistical step length a), so that

reaction can take place. The penetrating chain suffers the

same entropy penalties as the already reacted chains, i.e.

configurational restrictions due to stretching and the

necessity to overcome the free energy barrier of the brush

layer. Two possibilities are identified; firstly the increase in

grafting density is subject to diffusion control over the free

energy barrier, secondly control is exercised by the intrinsic

second order reaction kinetics of the reaction between the

functional end and the reactive sites. Regardless of whether

diffusion or reaction control prevails, both use the same

integral equation relating S to reaction time, i.e.ðj

0dj exp

mpðjÞ

kBT

� �¼ t=tc ð2Þ

where j is a normalised surface excess given by j ¼ zp=Rg ¼

NS=r0Rg: The free energy of the brush like layer at this

surface excess is given by, mpðjÞ=kBT and tc is a

characteristic time the form of which depends on whether

diffusion or reaction control prevails;

† diffusion control tc ¼ Rga=D with Rg the radius of

gyration of the polymer that has a diffusion coefficient,

D:

† reaction control tc ¼ Rg=ðak½R�Þ with k the second order

rate constant and [R] the concentration of reactive groups

fixed at the interface.

Eq. (2) can be used to obtain S as a function of t in the

following manner. Firstly, the integral in Eq. (2) is solved

numerically for selected values of j using values of

mpðjÞ=kBT tabulated by Shull [31], or in the case of high

values of S an approximation also given by Shull. Having

obtained values of the integral as a function of j; these are

converted to values of t via Eq. (2) (knowing tc). The values

of j are converted to S and thus the dependence on t

obtained. This model was later extended to account for a

finite concentration of reactive sites that are consumed

during reaction [29]. Only reaction control was considered

in this latter model and for this case the kinetics of grafting

has two behaviour regimes governed by a critical value of

the normalised surface excess, jc; defined as the surface

excess of tethered chains in the unperturbed state (i.e.

having the ‘mushroom’ configuration at the interface)

normalised by their bulk radius of gyration. In the absence

of any reverse reactions (explicitly included in the original

thesis [29]), and for j , jc

dj

dt¼ kf0½B� 1 2

Rgj

d0h

� �

�d

Rg

!2:1

1 2j

jc

þj

jc

exp2upðjcÞ

kBT

� �� ð3Þ

for j . jc

dj

dt¼ kf0½B� 1 2

Rgj

f0h

� �d

Rg

!2:1

exp2upðjÞ

kBT

� �ð4Þ

where f0 is the volume fraction of end functionalised chains

in the polymer mixture, [B] the concentration of reactive

sites at the interface, h is the thickness of the polymer film

containing the end-functionalised polymer and d the

thickness of the diffuse interface between the two polymers

that is given by the Helfand and Tagami equation [32].

An exhaustive treatment of the kinetics of interfacial

grafting has been provided by O’Shaugnessy and collabor-

ators [17–20] in a series of papers. The expression for the

kinetics of interfacial grafting is basically a second order

reaction kinetics model;

dS

dt¼ knBnA

where ni is the number density of reactive end functiona-

lised polymer i. The end functionalised polymers are

dispersed in polymer A or B that is identical with respect

to molecular weight but without the reactive ends, the

relaxation properties of functionalised and unfunctionalised

polymers are thus identical. The influencing factors are

contained within the expressions derived for the rate

constant, k: In deriving the expressions the molecular

weights, frictional and relaxational properties of both

polymers (functionalised and non-functionalised) are

assumed to be identical. The rate constant expressions

incorporate such aspects as local reactivity of the functional

groups, their residence time in the interfacial region and the

probability of two functional groups encountering each

other. The melt dynamics of the polymers have a significant

influence on the observed time dependence of S and the

statistical step length defines a critical local reactivity, other

factors incorporated are the time taken to diffuse a statistical

step length ðtaÞ and the ratio of the degree of polymerisation

to the entanglement value. Thus if the local reactivity Q is

less than the critical value Qc (mean field situation) then

k ¼ Qa3j ð5Þ

if Q . Qc diffusion control is evident and

k ¼ a4=ðtbðN=NeÞlnðN=NeÞÞ ð6Þ

where Ne is the entanglement degree of polymerisation of

the polymer.

However, like the extended Kramer model, these

equations only pertain to low values of S: For high values

we have

k ¼Qa3dðNa4S2Þexpð29Na4S2Þ

1 þ Qtaðd=aÞlnð1=ðSadÞÞð7Þ

The model developed by O’Shaugnessy accounts for

different concentrations of end groups in the two layers

but assumes that the relaxational properties at all time scales

M.L. Coote et al. / Polymer 44 (2003) 7689–7700 7691

are equal for each polymer. For polymers above the

entanglement molecular weight (a situation that prevails

here), the model can be summarised. In the early stages of

the reaction mean field conditions apply, the reaction

kinetics are second order and SðtÞ / t: If the functional

groups are sufficiently reactive, a depletion region may form

and the time dependence of S now depends on the spatial

extent of this depletion zone relative to the distance

explored by the chain in the various dynamic modes

inherent in the tube model of polymer dynamics. Predicted

dependences of S on reaction time are obtained by

integrating the second order rate equation using the

appropriate expression for k dependent on Q and the time

regime relevant to the dynamics of entangled polymer

melts. For time scales where Rouse or tube diffusion are the

dominant dynamics, the time dependence of the grafting

rate follows SðtÞ , t=ln t: For the time regime between these

two modes (‘breathing modes’ dominant) then SðtÞ , t1=2:

At sufficiently long times, greater than the terminal

relaxation time (reptation time) of the polymer, the kinetics

of grafting are controlled by the Fickian diffusion to the

interface of the end-reactive polymer present at the lower

concentration and SðtÞ , t1=2: When the interface becomes

grafted by block copolymer formation to such an extent that

the grafted molecules are separated by distances of Rg or

less, then increases in S becomes increasingly exponentially

suppressed with the growth of S; i.e. the rate of grafting

slows down. From a consideration of typical reactivities and

interface saturation times, O’Shaugnessy and Vavylonis

[20] predict that only mean field kinetics should be observed

up to interface saturation i.e. diffusion control of the grafting

reaction never intervenes. For low values of the grafting

density k is constant over the range of j but for high values

of S; a numerical integration is required using Eq. (7) as the

expression for k:

The final model for the kinetics of interfacial grafting in

polymer melts is due to Fredrickson and Milner [14,15] and

is similar to that of O’Shaugnessy et al. except that identical

concentrations of the end functionalised polymer in each

phase either side of the interface are presumed. This is a

condition that is not met by our experiments and hence we

do not consider this model in detail. In the very early stages

the growth in S is approximately linear with time. This

causes a depletion region near the interface and the growth

in S is controlled by the diffusion of polymer into the

interfacial region and SðtÞ / t1=2 in this region. The final

region is where the brush like layer at the interface has been

formed and the growth in S becomes very slow due to the

barriers to be overcome in penetrating the brush layer.

3. Experimental

3.1. Materials

Amine end group functionalised deutero polystyrene

(DPSNH2) was prepared by the reaction of living poly-

styrene with an a-bromo-v-aminopropane. A protected

amine was prepared by adding 2.5 equiv. of trimethyl

chlorosilane to a rapidly stirred mixture of 3-bromopropy-

lamine hydrobromide (0.1 mol) in dichloromethane with

3.5 equiv. of triethylamine added. The reaction was carried

out in a flask that had been thoroughly purged with dry

nitrogen and an atmosphere of dry nitrogen was maintained

during the overnight stirring of the reactant mixture. After

this time, dichloromethane and unreacted trimethyl chlor-

osilane were distilled off and after adding 100 ml of hexane

the mixture was filtered. The filtrate was twice washed with

100 ml portions of 5% w/w aqueous sodium bicarbonate and

finally with distilled water. Rotary evaporation removed the

hexane to leave the crude product in about 75% yield. This

was distilled under vacuum (,1 mm Hg) and the distillate

collected over the range 307–309 K. 1H NMR in deutero-

chloroform gave resonances at 0.05 ppm (Si-CH3), 1.9 ppm

(CH2), 2.95 ppm (N-CH2) and 3.3 ppm (BrCH2), all

consistent with the structure of the protected amine.

Deuteropolystyrene was prepared by anionic polymeris-

ation of deuterostyrene in benzene solution under high

vacuum using sec-butyl lithium as initiator. Polymerisation

was carried out overnight and then dry THF was added

(20% by volume) and the solution of living polymer cooled

to 273 K before adding 5 equiv. of the protected amine. The

now colourless solution was poured into a large excess of

methanol and the precipitated polymer filtered off, washed

with methanol and dried under vacuum. Deprotection of the

amine end group was achieved by refluxing a THF solution

of the dried polymer to which a small volume of dilute

hydrochloric acid had been added. Thin layer chromatog-

raphy of the resulting polymer using toluene/hexane (80:20)

as the eluting solvent indicated that end functionalisation

was quantitative. Three different molecular weight poly-

mers were synthesised by this means, DPSNH2250,

DPSNH2100, DPSNH250 the numbers indicating the

approximate molecular weight (in units of 103 g mol21).

Polymethyl methacrylate was prepared by the anionic

polymerisation of methyl methacrylate in THF solution

under high vacuum. The initiator was 1,1-diphenylhexyl

lithium and 10 M equiv. of lithium chloride were added to

control molecular weight and molecular weight polydis-

persity and the reaction carried out at ,195 K. On

completion of polymerisation, high purity carbon dioxide

was admitted to the reaction flask until atmospheric pressure

was reached. The solution was left overnight with constant

stirring at 195 K, thereafter the polymer was precipitated by

pouring the solution into a large excess of hexane, filtered

off, washed and dried in vacuum. The polymer produced

had a carboxylic acid group at one end and is indicated as

HPMMACOOH.

Hydrogenous polystyrene (HPS) with no functional end

groups was prepared by exactly the same procedure as for

the deuteropolystyrene except that the reaction was

terminated by addition of methanol rather than the protected


aminopropane. Polymethacrylic acid (PMAA) was pur-

chased from Polysciences, molecular weights and poly-

dispersities of all polymers used are given in Table 1.

3.2. Neutron reflectometry

Three series of experiments were carried out; (i) effect of

concentration on the grafting reaction of DPSNH2250 with

PMAA; (ii) influence of concentration of DPSNH2250 on

the grafting kinetics for the reaction with HPMMACOOH;

(iii) dependence of grafting kinetics on the molecular

weight of DPS-NH2 reacting with HPMMACOOH. For all

three experimental series, the samples consisted of bilayers

of the two polymers on polished silicon blocks that were

5 mm thick. The methacrylic layer was spun on to the

silicon block to form a film circa 700 A thick. For HPMMA-

COOH the solvent used was toluene, water being used as the

spin coating medium for PMAA. The thin films were then

held at 313 K under vacuum overnight to relax any stresses

due to spin coating. Upper layers of mixed HPS/DPSNH2

polymers were spin coated directly on to the acrylic layer

using 1,2,4-trimethyl benzene as the solvent. Ellipsometry

showed that the polystyrene layer thicknesses were circa

700–800 A, each bilayer specimen was then held at 453 K

under vacuum for defined times. Separate experiments

where 1,2,4-trimethyl benzene alone was spin coated on to

the acrylic polymer film showed that there was no change in

either thickness or surface roughness of the acrylic layer,

these latter parameters being determined by X-ray

reflectometry.

Neutron reflectometry data for each polymer couple were

obtained using the CRISP reflectometer on the ISIS pulsed

neutron source at the Rutherford Appleton Laboratory,

Chilton, UK. The neutron beam was collimated by slits

defined by translatable sheets of cadmium, the slit height

immediately before the specimen being 2 mm. By using

three different grazing angles of incidence the range of

momentum transfer, Q; normal to the sample surface

explored was , 1023 # Q= �A21 # 0:2 and the resolution

in Q; over all Q ranges was 4%. The lowest Q values were in

the region of total reflection ðRðQÞ ¼ 1Þ; and all data at

higher Q values was placed on an absolute scale using this

region of total reflectivity as calibration. For Q . 0:1 �A21;

the reflectivity was essentially constant at the background

value mainly due to incoherent scattering from the polymer

couple. Reflectivity data were analysed using Abeles

modification of the optical matrix method [33] that

calculates exactly the reflectivity from a model of the

polymer couple and where possible roughness at the air-film

and film substrate can be incorporated as Gaussian broad-

ening. The total thickness of the bilayer was simulated by a

series of layers of constant composition. In the region of the

interface between the polystyrene and acrylic layers, a

functional form (Eq. (8) below) was used to describe the

region where an excess of deuterated polymer was formed

due to reaction at the interface.

4. Results

The variation of the scattering length density (SLD)

normal to the polymer bilayer surface was modelled as a

series of stacked lamellae with the SLD of each lamellar

layer being calculated from its volume fraction composition

[21,22,34]. Near the interface between the two polymers,

the interfacial excess layer due to grafting was approxi-

mated by a hyperbolic tangent distribution in which the

volume fraction distribution of DPSNH2 was described by

fðzÞ ¼ fbulk þfint 2 fbulk

2

� �tanh½ðz þ zoff 2 tPSÞ=w� ð8Þ

where fbulk is the volume fraction of DPS-NH2 in the

polystyrene top layer, fint the value at the interface with the

acrylic layer. The shape of the distribution is controlled by

zoff and w; the former being the thickness of the distribution

at ðfint 2 fbulkÞ=2 and w is a measure of the overlap between

the grafted layer and the bulk polystyrene layer which has a

thickness, tPS: A schematic of a SLD distribution for this

model is shown in Fig. 2. Reflectivity profiles were

calculated for this model and fitted to the experimental

data by adjusting fint; zoff and w using a non-linear least

squares fitting algorithm. The thickness of the upper

polystyrene layer and the total thickness of the bilayer

were allowed to vary to a small extent (^10% of measured

thickness) as part of the fitting process to account for any

physical relaxation of the polymers at the elevated

temperatures where reaction took place. The interface

between the two polymers before annealing at elevated

temperatures has a small intrinsic roughness of circa 1.5 nm

from the bilayer preparation. Typical examples of the fits to

the data are shown in Fig. 3(a) and the corresponding

volume fraction distributions of DPSNH2 resulting from the

best fit the reflectometry data are shown in Fig. 3(b), the

small variation in the bulk concentration of DPSNH2 is

within the error of the fitting to the reflectivity data. From

the volume fraction distribution, the interfacial excess of

Table 1

Molecular weights and polydispersity of polymers

Polymer Mw (103 g mol21) Mw=Mn

DPSNH2250 230 1.02

DPSNH2100 95.1 1.04

DPSNH250 43.4 1.03

HPS250 228.7 1.08

HPS100 102.5 1.03

HPS50 46.0 1.03

HPMMACOOH 124 1.04

PMAA 100 ,2


DPSNH2 was obtained from

zp ¼ð1

0ðfðzÞ2 fbulkÞdz ð9Þ

and the ellipsometric thickness, L; of the interfacial excess

layer formed by reaction was calculated from

L ¼1

zp

ð1

0zðfðzÞ2 fbulkÞdz ð10Þ

4.1. DPSNH2—polymethacrylic acid combination

This pairing corresponds most closely to the situation for

which the original Kramer model was developed, i.e. the

presence of an essentially infinite number of one reactive

group (–COOH) and a finite number of the second (–NH2).

Using the bulk density of PMAA and the known molecular

weight of the polymer, the average number of –COOH

groups per nm2 at the interface with the DPSNH2/HPS layer

is circa 3.5. Using an average upper layer thickness of

100 nm and considering the range of the DPSNH2

concentrations in the upper layer, the number of amine

ends available ranges from circa 5 £ 1022 to

10 £ 1022 nm22, far smaller than the number of –COOH

groups. Grafting densities obtained from the variation of zp

with time are shown in Fig. 4(a) for all three concentrations

of DPSNH2250 used. For each of these the data are rather

similar, a rapid increase in S to values of circa 2 £ 1022–

2.5 £ 1022 nm22, thereafter S remains constant at these

values. The layer thickness (Fig. 4(b)) qualitatively shows

the same behaviour but with a larger variation in the actual

values, although an asymptotic interfacial excess layer

thickness of ,13 nm at long reaction times seems to be

approached for the 10 and 30% DPSNH2 systems.

4.2. DPSNH2–HPMMACOOH combination

4.2.1. Concentration dependence

For the molecular weight of HPMMACOOH employed,

Fig. 2. Scattering length density over the polymer bilayer at a point where a finite extent of reaction is evident.

Fig. 3. (a) Typical fits (solid line) to neutron reflectivity data. For zero time

the data are absolute, longer reaction times are artificially displaced by two

decades to lower reflectivity to aid clarity. (b) Volume fraction distribution

of DPSNH2 obtained from fits to reflectivity data.


the average number of end carboxyl groups available at the

interface is ,2.8 £ 1022 nm22, assuming that all the

carboxyl groups are available for reaction, i.e. they have

the correct orientation and proximity to the interface. A 10%

concentration of DPSNH2250 in the upper layer has an

approximately equal number of NH2 end groups available in

the total thickness of the polystyrene upper layer. The actual

time dependence of the grafting density obtained for the

four concentrations used is shown in Fig. 5(a). For all

concentrations the grafting curves are similar, a rapid

increase in the early stages but after circa 7 h the rate of

grafting is considerably reduced but not to zero for

concentrations of DPSNH2 of 10% w/w and greater. Over

the reaction times investigated here, the nominal maximum

value of S possible ( ¼ number of –COOH groups nm22

calculated above) is approaching twice the actual maximum

value of S observed experimentally even though for the

27% DPSNH2 in HPS the –NH2 ends far exceeds the

number of –COOH groups available. Values of the layer

thickness, Fig. 5(b), are much less regular in their variation

with reaction time although the largest values of L observed

are associated with the highest values of S; a possible

indication of some stretching of the grafted chains. The

interfacial layer thickness for the 5% DPSNH2 is larger than

that for the 10% concentration but the grafting density is

lower. We can only attribute this anomalous result to the

possibility that the –COOH groups at the interface have

regions where their concentration is higher and thus the

local grafting density is much higher than the average

leading to a more highly stretched configuration. Addition-

ally, reaction would be probable for such regions of high

concentration. Higher concentrations of DPSNH2 lead to the

interface becoming more evenly covered with reacted

polymer molecules.

4.2.2. Influence of molecular weight of DPSNH2

To investigate the role of molecular weight on the

interfacial grafting kinetics, DPSNH2100 and DPSNH250

were mixed with HPS of equivalent degrees of polymeris-

ation. Additionally, the concentration of each DPSNH2 was

adjusted so that the molar concentration of –NH2 end

groups was the same for all the molecular weights of the

Fig. 4. (a) Grafting density of DPSNH2250 at the interface with PMAA as a

function of reaction time. (b) DPSNH2250 layer thickness changes as a

function of the reaction time at the HPMAA interface.

Fig. 5. (a) Grafting density as a function of reaction time for DPSNH2250 at

the interface with HPMMACOOH. (b) DPSNH2250 layer thickness

dependence with reaction time at the HPMMACOOH interface.


deutero polymer used. For the lowest molecular weight

DPSNH2, the values of S are significantly larger than for the

two higher molecular weights but grafting densities for

DPSNH2100 are of the same magnitude as those of

DPSNH2250, (Fig. 6(a)), however, we note the large scatter

in the values of S at short reaction times for the DPSNH2100

for which we can attribute no physical cause but may reflect

insensitivity in the model used to describe the interfacial

layer formed by reaction. Layer thicknesses, Fig. 6(b), are

again somewhat scattered with no discernible trend in even

the asymptotic layer thickness at long reaction times except

that the largest layer thickness is observed for the lowest

molecular weight polymer.

5. Discussion

Of the small amount of other experimental data [13,16,

29,35–38] available on the grafting kinetics at the interface

between immiscible polymer melts, none conform exactly

to the systems investigated here. In the earlier studies, the

reactive polymers were of much lower molecular weight

than those used here and were usually mixed in an

unreactive host of considerably higher molecular weight.

Such combinations are very different to the conditions

presumed in the models for interfacial grafting described by

O’Shaugnessy and Fredrickson and Milner, wherein, the

intrinsic polymer melt dynamics play a significant role.

Experimental data obtained for polymers with lower

molecular weights than used here gave values of S up to

an order of magnitude larger than observed by us and in one

case larger by two orders of magnitude. However, in the last

case the high value of zp was attributed to a very rough

interface being produced as a result of the reduction of the

interfacial tension and eventual ‘pinch out’ of polymer from

the interface. Nonetheless, all earlier experimental data

shows the same dependence of S with time as that exhibited

by all the combinations that we have investigated. At low

reaction times, the rate of grafting is constant and a linear

increase in S is noted, the rate of grafting then decreases

rapidly over a short time span to a significantly smaller rate

of grafting that approaches zero.

All of the theoretical models developed for interfacial

grafting kinetics include many factors influencing the value

and dependence of S on time. Some factors are common to

all theories, e.g. concentration of reactive polymer, rate

constant of the second order reaction, thickness of the

interfacial region, where some small degree of mixing takes

place in the absence of any interfacial grafting. However,

individual theories incorporate additional specific factors.

For example, the theory due to O’Shaugnessy includes the

entanglement degree of polymerisation and the relaxation

time of a monomer unit for the purpose of accurately

describing the polymer melt dynamics. The value of this

latter parameter has some uncertainty. The two theories that

originate from Kramer require values for the chemical

potential of a grafted brush-like layer at each value of S to

define the resistance to approaching reactive polymer. In all

theories, the major uncertainty is the concentration at the

interface of reactive groups, both fixed i.e. groups with an

essentially fixed concentration, the carboxylic acid groups

here, and mobile, i.e. those groups whose concentration will

be significantly influenced by reaction, the DPSNH2 units

for the combination discussed here. To provide quantitative

comparison for the influence of the bulk concentration of

reacting species a phenomenological equation can be used

to provide parameters for comparison. The equation

employed is [38]

S ¼ Að1 2 expð2t=tÞÞ ð11Þ

where A and t are characteristic of the molecular weight and

concentration of DPSNH2 in the upper polystyrene layer

and we anticipate

ta1=k½COOH� ð12Þ

For DPSNH2250 on PMAA the value of A is essentially

constant at 0.022 ^ 0.005 nm22 for all the concentrations

Fig. 6. Molecular weight dependence of grafting density (a) and layer

thickness (b) for DPSNH2 reacting with HPMMACOOH whilst the

concentration of amine end groups is maintained constant.


of DPSNH2250 considered. When the same DPSNH2250 is

on the HPMMACOOH film, a definite, albeit weak, increase

in A is observed with increasing concentration, c; of the

deuteropolymer in the upper layer given by;

A ¼ 5:4 £ 1024 þ 4:6 £ 1024c

with c in wt%. These different behaviours reflect the large

differences in the concentration of – COOH groups

available for reaction. In the PMAA, their large excess

over the available –NH2 groups results in no dependence on

the concentration of these latter groups. Whereas, for the

HPMMACOOH the carboxyl and amine group concen-

trations are of the same order of magnitude and any change

in either will have an influence on the observed grafting rate

and hence the value of A in Eq. (11). If Eq. (12) is a valid

description of the characteristic time then values of t for

DPSNH2250 on HPMMACOOH should be larger than

when the lower layer is HPMAA. For the latter combination

the average value of t is 0.5 ^ 0.2 h21 whereas, when

HPMMACOOH formed the lower polymer layer the values

of t observed for the four concentrations explored is

1.9 ^ 0.3 h21. Hence, the anticipated increase in magnitude

is observed but not in proportion to the ratio of the surface

concentrations of the –COOH groups nominally available

based on the earlier figures given. The molecular weight of

the DPSNH2 influences both A and t but the latter is

essentially independent of molecular weight within exper-

imental error, the scaling relations obtained from the data

are;

A ¼ 0:25 M20:25; t ¼ 2:4 M20:02

Evidently, the influence of molecular weight is primarily

exercised through the parameter A; with a decrease in the

ultimate extent of grafting with molecular weight being

observed.

A qualitative comparison of the experimental data with

the predictions of the various theories can be made if values

are assumed for the various parameters that each theory

uses. Thus for both theories that originate from Kramer’s

group a value for the rate constant is needed and we have

assumed a value of 0.18 l mol21 s21, a value that Kramer

reported earlier on the basis of ion beam analysis between

epoxide and amine groups, other parameters such as

statistical step length, diffusion coefficients, extent of

diffuse interfacial layer etc, are accessible from other

sources. For the extended Kramer theory, the thickness of

the polystyrene layer (which defines the ultimate number of

reactive molecules available) has been fixed at 100 nm and

the equilibrium coefficient for the reverse reaction that is

incorporated in the full theory has been set to a value of

unity on the assumption of a complete absence of reverse

reactions. For the O’Shaugnessy model values of the

unknowns Q and ta are even more uncertain, the only

guidance provided being that their product has a magnitude

of ,10211, we have used 0.1 as the value of Q and 10210 s

for the value of ta: Fig. 7(a)–(c) shows the dependence of S

on reaction time for each of these models where the

concentration of one of the reaction polymers has been

varied whilst maintaining the degree of polymerisation of

both polymers constant. All models predict that the extent of

grafting should be reduced as the concentration of one of the

reacting polymers is reduced. Comparing these predictions

with the data of Fig. 5(a) the original Kramer model seems

to be the most appropriate since it suggests an early

approach to the saturation extent of grafting Ssat that is

observed by experiment. The O’Shaugnessy model predic-

tions appear to be very distant from approaching a Ssat value

and changing the magnitude of the model’s parameters to

accelerate the approach to Ssat increases the rate of grafting

in the early stages to values far larger than actually

observed. The extended Kramer model is evidently

approaching Ssat at longer reaction times. We note that

the values of S predicted by all three models are of the same

magnitude as the experimental data, but larger by a factor of

two compared to the observed values of S: Fig. 7(d)–(f)

shows the influence of varying the degree of polymerisation

but keeping the molar concentration of reactive end

constant. Clear differences are apparent now between the

original Kramer model which predicts that the higher

molecular weight polymer should have the larger values of

Ssat; moreover, the initial rate of grafting is essentially

identical for all molecular weights. This does not agree with

the predictions of the O’Shaugnessy or extended Kramer

models where now the highest molecular weight polymer

should have the lower values of Ssat and the rate of grafting

at the interface is also reduced as the molecular weight of

the reacting polymer increases. The experimental data of

Fig. 6(a) has the smaller values of Ssat associated with the

higher molecular weight DPSNH2, the data at earlier

reaction times is too scattered to state with confidence that

the rates of grafting also reduce as molecular weight

increases, however, the initial rate for the DPSNH250 does

appear to be larger than that of the DPSNH2250 polymer.

Since the O’Shaughnessy model shows little sign of

approaching a Ssat value within the reaction times used, only

the extended Kramer model has been compared to our data.

Initially, it is assumed that all the –COOH groups of the

HPMMACOOH were available and the influence of the

second order rate constant over the range 0:1 # k=l mol21

s21 # 0:2 is shown in Fig. 8 together with some of our

experimental values of S: Although, the initial rates of

grafting observed and calculated are in reasonable agree-

ment with each other, there is no agreement in Ssat; the

predicted values of S continuing to increase long after the

experimental values have saturated. The possibility that

the available –COOH groups may be far smaller is shown in

Fig. 8(c) where fB is the fraction of these groups available

for reaction. Values of fB less than one have no effect on the

time at which Ssat is reached and moreover the rate of

grafting and the ultimate value of Ssat clearly falls below the


experimental values and thus this cannot be the source of the

observed behaviour.

The major difference between theory and experiment is

the prediction of the value of Ssat and hence the time at

which this value is reached. Two factors are cited as the

source of the reduction in grafting rate, firstly, a depletion of

unreacted chain ends in the neighbourhood of the interface

and secondly saturation of the interface by grafted

molecules preventing the approach of unreacted chains to

within the reaction distance of the interface. The diffusion

coefficient of DPSNH2250 is anticipated to be little altered

from that of unmodified polystyrene and a diffusion

coefficient of ,2.2 £ 10214 cm2 s21 is expected. This

suggests that the time for a DPSNH2 molecule to diffuse

Fig. 7. Simulations of models for the kinetics of interfacial reactions between immiscible polymers, predicted influence of weight fraction ðf Þ of reacting

polymer for (a) original Kramer model; (b) O’Shaugnessy model; (c) extended Kramer model. Influence of degree of polymerisation of reacting polymer for (d)

original Kramer model; (e) O’Shaugnessy model; (f) extended Kramer model.


from one side of the 100 nm thick polystyrene layer to the

interface is less than 20 min and consequently the DPSNH2

chains are always in diffusion equilibrium with the interface

and thus depletion of reactive polymer near the interface

appears to be remote. When the interface becomes

saturated, the grafted layer acquires a brush-like nature

and incoming ungrafted chains have to stretch to traverse

the brush layer and the entropic penalty entailed constitutes

the barrier to reaction that slows the grafting reaction. Two

methods of defining Ssat are quoted; firstly when the average

distance between grafting points is equal to the radius of

gyration of the grafting polymer, i.e. Ssat ¼ R22g ; secondly

Ssat , ðN1=2a2Þ21 where a is the statistical step length of the

polymer. Values of Ssat calculated by these two approaches

are given in Table 2 together with the values observed

experimentally for the three molecular weights of DPSNH2.

It is evident that the experimental values of Ssat are closer to

the predictions based on Ssat being controlled by the radius

of gyration possibly due to a ‘masking’ of reaction sites at

the interface by segments of grafted polymer.

6. Conclusions

The extent of reaction at the interface between two end—

functionalised immiscible polymers, polystyrene and poly-

methyl methacrylate, has been determined using neutron

reflectometry. Aspects investigated include the concen-

tration of ‘fixed’ reacting groups (–COOH), concentration

of ‘mobile’ reacting groups (–NH2) and the molecular

weight of the polystyrene with a primary amine end

function. The use of neutron reflectometry has provided a

detailed description of the interfacial excess layer when the

deuterated end functionalised polystyrene reacted with the

carboxylic acid groups of the acrylic polymers, a modified

hyperbolic tangent profile providing the best description of

the volume fraction distribution of reacted polymer. From

values of the interfacial excess calculated from these

volume fraction profiles, the extent of grafting, S; as a

function of reaction time has been calculated. All polymer

combinations have a generic dependence of S on time, i.e. a

rapid increase in S at short reaction times with Ssat also

being reached quite early in the reaction and further

increases in S being either very small or non-existent.

When the concentration of fixed reacting groups is in large

excess over that of the mobile groups, there is essentially

negligible dependence of S on any changes in concentration

of the mobile reacting groups. However, when both fixed

and mobile reacting groups are present at concentration of

the same, small magnitude, the values of S and Ssat are

noticeably larger for higher concentrations of the mobile

polymer when the concentration of the fixed reacting groups

is held constant. Under the same circumstances of low

concentrations of mobile reacting groups, changing the

molecular weight of these mobile groups whilst maintaining

a constant overall concentration of reactive end groups’

results in the larger values of S being observed for the lower

molecular weight polymer. This agrees with the predictions

of two of the current theories that attempt a quantitative

description of grafting kinetics at the interface between

immiscible polymers. An exact coincidence between the

Fig. 8. Comparison of the predictions of extended Kramer theory with

experimental data. Effect of varying the second order rate constant for the

highest (a) and lowest (b) molecular weight DPSNH2 polymers used. The

role that the fraction of reactive end groups, fB; in the acrylic layer is made

evident in (c).


most appropriate theory and experimental data is not

obtained either by adjusting the second order rate constant

or the effective concentration of fixed reacting groups. By

varying the second order rate constant, reasonable agree-

ment with the initial rate of grafting can be obtained but Ssat

values are not reproduced. From the definitions of where

the effects of Ssat should become evident it appears that the

notion of brush-like layer formation being the source of the

reduction in the rate of grafting is not upheld and other

factors are at work in reducing the increase of S at long

reaction times.

Acknowledgements

We thank EPSRC for the support of this research and

CCCRC for the provision of neutron beam facilities.

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Table 2

Molecular weight dependence of calculated and experimental values of Ssat for DPSNH2 reacting at the interface with HPMMACOOH

Polymer Ssat from Rg (nm22) Ssat from ðN1=2a2Þ21=nm22 Ssat observed/nm22

DPSNH2250 5.7 £ 1023 4.9 £ 1022 1.1 £ 1022

DPSNH2100 1.4 £ 1022 7.6 £ 1022 1.4 £ 1022

DPSNH250 3.0 £ 1022 11.3 £ 1022 2 £ 1022


Michelle L. Coote et al., Polymer, 44, (2003), 7689 - 7700.

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